The invention relates to an apparatus and a method for determining the velocity vector of a remotely sensed object using either sound, in particular ultrasound, or electromagnetic radiation. The movement of the object is determined by emitting and receiving a pulsed field focused in the direction of the velocity vector. By using a number of pulse emissions, the inter pulse movement can be estimated and the velocity found from the estimated movement and the time between pulses. The invention is based on the principle of using a directionally focused field for making the received signal influenced by motion along the direction of the movement.
Medical ultrasound is extensively used for studying flow dynamics in the human body by using color flow mapping. The technique displays a color image of the flow superimposed on the normal anatomic B-mode image. Traditionally, the velocity component along the ultrasound beam direction is measured, and a flow transverse to the beam is not displayed, since it is not measured or estimated. An example of this is shown in FIG. 1, where the flows in the carotid artery and the jugular vein are displayed. The image is acquired with a convex array transducer, and the angles between flow direction and the ultrasound beam change over the image. Notice the change of estimated flow direction around the dashed line in both vessels due to the change of angle between the flow and the ultrasound beam. This is one of the main limitations of current ultrasound flow systems, since most vessels are parallel to the skin surface, and therefore it is a problem to get a sufficiently small angle between the flow and the beam. Also the flow is often not parallel to the vessel surface, and it is therefore difficult, if not impossible, to estimate the correct angle and compensate for it [1]. In European patent application EP 616 231 [2] the velocity is found through a cross-sectional area using a 2D matrix transducer that can focus on the individual areas in the cross-section. The volume flow through the cross-section is then found, but still only the velocity in direction of the ultrasound beam is estimated. Several authors have attempted to remedy this artifact. Fox [3] suggested using two beams to find the transverse component. The system works well for large transducers and investigations close to the transducer, but the variance of the transverse component increases for situations with large depths and smaller transducers as used in cardiac scanning through the ribs. Trahey and co-workers [4] have suggested using speckle tracking in which a small search region in one image is correlated or compared to a subsequent image. This approach has problems in terms of frame rate, since images are compared, and the resolution of the velocity estimates can be low. Newhouse et al. [5] developed a method in which the total bandwidth of the received signal is affected by the transverse velocity. It is, however, often difficult to find this bandwidth due to the inherent noise in the signal.
Of special interest is the working by Bonnefous [6], which uses a number of parallel beams to find the transverse velocity. The approach does, however, not work for a velocity that is not orthogonal to the ultrasound beam direction.
In this invention a new technique using a focused signal in the direction of the velocity is used. The velocity is then found by acquiring two or more of these focused signals and cross correlating them to find the displacement between pulse emission, whereby the velocity can be determined.
This section summarizes the article written in 1988 by Bonnefous [6], where a method for estimating the transverse velocity was suggested.
Transverse velocity estimation must perform a signal processing, where the effect of axial motion is negligible compared to the transverse one. The idea presented by Bonnefous requires a broad beam in emission (a plane ultrasound wave front), and a number of parallel identical beams, separated by a pitch w in the transverse direction, are generated in reception, see FIG. 2.
For a given depth z, the signal received Sn(x,t) from the beam centered in x=0 is
xe2x80x83Sn(0,t)=∫p(x,t)Dn(x)dxxe2x80x83xe2x80x83(1)
where p(x,t) is the response of a scatterer located at x in the ultrasound beam centered at x=0, and Dn(x) is the scatterer distribution at the instant nTprf, where Tprf is the pulse repetition period. In the same way, the signal received from the beam centered at x=w is
Sn(w,t)=∫p(xxe2x88x92w,t)Dn(x)dxxe2x80x83xe2x80x83(2)
If only a transverse uniform motion of the scatterers in considered, the displacement between two consecutive pulses nTprf and (n+1)Tprf will give the relation for the distribution of the scatterers
Dn+1(x)=Dn(xxe2x88x92vxTprf)xe2x80x83xe2x80x83(3)
where vx is the velocity of the scatterers. Combining equations (2) and (3) gives
Sn+1(0,t)=∫p(x,t)Dn+1(x)dx=∫p(x,t)Dn(xxe2x88x92vxTprf)dx=∫p(x+vxTprf,t)Dn(x)dxSn+1(0,t)=Sn(xe2x88x92vxTprf,t)xe2x80x83xe2x80x83(4)
For a beam centered in x=w the relation between the consecutive signals is
Sn+1(w,t)=Sn(wxe2x88x92vxTprf,t)xe2x80x83xe2x80x83(5)
The signal received in x=w at the pulse time (n+1)Tprf is, thus, the same as the signal received in a beam centered in x=wxe2x88x92vxTprf at the pulse time nTprf.
The correlation between the two signals p(x,t) and p(xxe2x88x92w,t) is an averaging of the received signals over the random scatterer distributions. The cross-correlation of the received signals from two adjacent signals is                                                                                           C                  1                                ⁡                                  (                  w                  )                                            =                                                ∑                  n                                ⁢                                                      ∫                                          t                      0                                                                                      t                        0                                            +                                              Δ                        ⁢                                                  xe2x80x83                                                ⁢                        t                                                                              ⁢                                                                                    S                        n                                            ⁡                                              (                                                  0                          ,                          t                                                )                                                              ⁢                                                                  S                                                  n                          +                          1                                                                    ⁡                                              (                                                  w                          ,                          t                                                )                                                              ⁢                                          xe2x80x83                                        ⁢                                          ⅆ                      t                                                                                                                                              =                                                ∑                  n                                ⁢                                                      ∫                                          t                      0                                                                                      t                        0                                            +                                              Δ                        ⁢                                                  xe2x80x83                                                ⁢                        t                                                                              ⁢                                                                                    S                        n                                            ⁡                                              (                                                  0                          ,                          t                                                )                                                              ⁢                                                                  S                        n                                            ⁡                                              (                                                                              w                            -                                                                                          v                                x                                                            ⁢                                                              T                                prf                                                                                                              ,                          t                                                )                                                              ⁢                                          xe2x80x83                                        ⁢                                          ⅆ                      t                                                                                                                                                                                C                  1                                ⁡                                  (                  w                  )                                            =                                                C                  0                                ⁡                                  (                                                            w                      -                                                                        v                          x                                                ⁢                                                  T                          prf                                                                                      ,                    t                                    )                                                                                        (        6        )            
where                     C        0            ⁡              (        w        )              =          ∑                        ∫                      t            0                                              t              0                        +                          Δ              ⁢                              xe2x80x83                            ⁢              t                                      ⁢                                            S              n                        ⁡                          (                              0                ,                t                            )                                ⁢                                    S              n                        ⁡                          (                              w                ,                t                            )                                ⁢                      xe2x80x83                    ⁢                      ⅆ            t                                ,
is the autocorrelation function averaged over a number of received lines, where the line number is denoted by n. The interval (t0,t0+xcex94t) is the range gate selected for the received signals. Equation (6) show that the shift of C1 compared with C0 is the transverse displacement between the instants nTprf and (n+1)Tprf. Therefore, the maximum of C1(w) is C1(vxTprf)=C0(0).
For the general case, in which both axial and transverse motion takes place, the equation that relates the received signals from two successive pulses will be                                           S                          n              +              1                                ⁡                      (                          w              ,              t                        )                          =                              S            n                    ⁡                      (                                          w                -                                                      v                    x                                    ⁢                                      T                    prf                                                              ,                              t                -                                  xe2x80x83                                ⁢                                                      2                    ⁢                                          v                      z                                        ⁢                                          T                      prf                                                        c                                                      )                                              (        7        )            
Here ts=2vzTprf/c, is the time shift for the axial motion.
The cross-correlation and autocorrelation functions are generalized to two-dimensional functions and their expressions are                                                                                                                                                             C                        1                                            ⁡                                              (                                                  w                          ,                          u                                                )                                                              =                                          xe2x80x83                                        ⁢                                                                  ∑                        n                                            ⁢                                                                        ∫                                                      t                            0                                                                                t                                                          0                              +                                                              Δ                                ⁢                                                                  xe2x80x83                                                                ⁢                                t                                                                                                                                    ⁢                                                                                                            S                              n                                                        ⁡                                                          (                                                              0                                ,                                t                                                            )                                                                                ⁢                                                                                    S                                                              n                                +                                1                                                                                      ⁡                                                          (                                                              w                                ,                                                                  t                                  +                                  u                                                                                            )                                                                                ⁢                                                      xe2x80x83                                                    ⁢                                                      ⅆ                            t                                                                                                                                                                                                          xe2x80x83                                        ⁢                                          (                      8                      )                                                                                                                                        =                                          xe2x80x83                                        ⁢                                                                  ∑                        n                                            ⁢                                                                        ∫                                                      t                            0                                                                                                              t                              0                                                        +                                                          Δ                              ⁢                                                              xe2x80x83                                                            ⁢                              t                                                                                                      ⁢                                                                                                            S                              n                                                        ⁡                                                          (                                                              0                                ,                                t                                                            )                                                                                ⁢                                                                                    S                              n                                                        ⁡                                                          (                                                                                                w                                  -                                                                                                            v                                      x                                                                        ⁢                                                                          T                                      prf                                                                                                                                      ,                                                                  t                                  -                                                                      xe2x80x83                                                                    ⁢                                                                                                            2                                      ⁢                                                                              v                                        z                                                                            ⁢                                                                              T                                        prf                                                                                                              c                                                                    +                                  u                                                                                            )                                                                                ⁢                                                      xe2x80x83                                                    ⁢                                                      ⅆ                            t                                                                                                                                                                                                          xe2x80x83                                        ⁢                                          (                      9                      )                                                                                                                                                                                      C                        0                                            ⁡                                              (                                                  w                          ,                          u                                                )                                                              =                                          xe2x80x83                                        ⁢                                                                  ∑                        n                                            ⁢                                                                        ∫                                                      t                            0                                                                                                              t                              0                                                        +                                                          Δ                              ⁢                                                              xe2x80x83                                                            ⁢                              t                                                                                                      ⁢                                                                                                            S                              n                                                        ⁡                                                          (                                                              0                                ,                                t                                                            )                                                                                ⁢                                                                                    S                              n                                                        ⁡                                                          (                                                              w                                ,                                                                  t                                  +                                  u                                                                                            )                                                                                ⁢                                                      xe2x80x83                                                    ⁢                                                      ⅆ                            t                                                                                                                                                                                                          xe2x80x83                                        ⁢                                          (                      10                      )                                                                                                                              xe2x80x83                                                          xe2x80x83            
The relation between the cross-correlation and the autocorrelation is                                           C            1                    ⁡                      (                          w              ,              u                        )                          =                              C            0                    ⁡                      (                                          w                -                                                      v                    x                                    ⁢                                      T                    prf                                                              ,                              u                -                                  xe2x80x83                                ⁢                                                      2                    ⁢                                          v                      z                                        ⁢                                          T                      prf                                                        c                                                      )                                              (        11        )            
The two-dimensional determination of the velocity vector is performed by first finding the axial velocity and then the transverse component.
1. Axial velocity measurement: C1(0,u) is calculated and then, the time position of the correlation peak is determined as                                           Max            u                    ⁡                      [                                          C                1                            ⁡                              (                                  0                  ,                  u                                )                                      ]                          =                              C            1                    ⁡                      (                          0              ,                              xe2x80x83                            ⁢                                                2                  ⁢                                      v                    z                                    ⁢                                      T                    prf                                                  c                                      )                                              (        12        )            
2. Transverse velocity measurement: Fixing the value of the time coordinate to be u=2vzTprf/c in C1(w,2vxTprf/c), the peak for the transverse correlation is determined as                               Max          w                [                                            C              1                        (                          w              ,                              xe2x80x83                            ⁢                                                2                  ⁢                                      v                    z                                    ⁢                                      T                    prf                                                  c                                      ]                    =                                    C              1                        ⁡                          (                                                                    v                    x                                    ⁢                                      T                    prf                                                  ,                                  xe2x80x83                                ⁢                                                      2                    ⁢                                          v                      z                                        ⁢                                          T                      prf                                                        c                                            )                                                          (        13        )            
This process can be generalized to measure the three-dimension velocity vector. New parallel beams along the y-axis should be used, and the cross-correlation function will be a three-dimensional function of the type C1(w,h,u). The problem with this approach is, however, that a spatially invariant velocity field is assumed, which is not the case in the human body.
This section describes the approach of the invention for finding the transverse component of the blood velocity. The invention presupposes that the direction of movement is known. In medical ultrasound a two-dimensional image including a blood vessel of interest is produced. The operator will then manually indicate the position and direction of the blood vessel to the system, or this information can be obtained automatically.
In a first embodiment of the invention, wave energy is emitted in a predetermined direction towards a moving object or a collection of moving objects, which will interact with the wave energy, whereby the wave energy will be scattered or reflected. Moving objects thus interacting with emitted wave energy are often referred to as xe2x80x9cscatterersxe2x80x9d. Scattered or reflected wave energy will be received and processed to yield the desired estimate or measurement of velocity of the moving object or a collection of moving objects. The velocity of any scattering or reflecting object, whether emitting it self or not, can be measured.
The main idea of the first embodiment of the invention is the creation of a plurality of focal points, which together form a focused line or beam in the direction of the velocity vector that will track the motion of the scatterers. The generation of this focused beam requires a broad beam in emission and multiple foci along the line in reception. This can be achieved with a multi-element transducer. The focusing line is situated over the region of interest, where the motion of the scatterers occurs, see FIG. 3. The method of the invention presupposes that scatterers, whose motion is tracked, have the same velocity along the whole length of the line. When measuring a laminar parabolic flow or other spatially variant velocity fields, the focus line therefore has to be oriented in the direction of the flow lines.
The lateral beam is calculated during reception by delaying and adding responses from the individual elements of the array. The delays are found for each focus point by calculating the time it takes for the ultrasound wave to travel from each transducer elements to the focus point and back to the transducer. Lateral beams are in this way constructed for each of the emitted pulses.
The velocity is estimated from the cross-correlation of two consecutive lateral signals. Hereby the displacement of the signals corresponds to an estimate of the distance traveled by the scatterers in the lateral beam direction. Since the lateral beams are situated along the flow stream-lines, the complete velocity magnitude can be directly estimated.
In a second embodiment the velocity of a moving object or a collection of moving objects emitting wave energy while moving, is measured. No emission of wave energy is required, but rather the wave energy emitted by the moving object is received and processed to yield the desired estimate or measurement of velocity of the moving object or a collection of moving objects. The main idea of the second embodiment of the invention is the creation of a plurality of focal points, which together form a focused line or beam in the direction of the velocity vector that will track the motion of the emitting object or objects.